Introduction.\(–\) 
The hydrodynamic theory is an effective coarse-grained formulation of the underlying microscopic dynamics at the long-wavelength limit, that has
served for decades as an efficient and accessible tool for a vast range of problems in theoretical physics. However convenient, the relativistic extension of the first-order dissipative Navier-Stokes (NS)
formalism introduced by Landau-Lifshitz (LL) [1]} and Eckart [2]}, encounters severe issues with instability [3]}, [4]}, [5]} and superluminal signal propagation,
which pose serious limitation to the practical application of the theory. Later on, second-order Muller-Israel-Stewart (MIS) theory [6]}, [7]} and some of its extended versions [8]}, [9]}, [10]}, [11]} are introduced to remedy these problems. Only recently, several studies have proposed [12]}, [13]}, [14]}, [15]}, [16]}, [17]} a first-order stable and causal theory by defining the out of equilibrium hydrodynamic variables in
a general frame other than LL or Eckart through their postulated constitutive relations that include both time and space gradients.
